Arteriosclerosis is any hardening (and loss of elasticity) of large arteries and arterioles (small arteries). It is often due to hypertension.
Artherosclerosis is a hardening of an artery specifically due to an atheromatous plaque. Atherosclerosis is the most common form of arteriosclerosis. Atherosclerosis is characterised by a thickening of the intima with plaques that can contain lipid-laden macrophages ("foam cells"). The plaques contain free lipid (cholesterol, etc.) and are prone to calcification and ulceration.